1 / 121

Econ 240C

Econ 240C. Lecture 14. ARCH-GARCH Structure?. Outline. Part I: Conditional Heteroskedasticity: example Part II: Detecting ARCH Part III: Modeling ARCH & GARCH Part IV: Estimating GARCH. Part I. Conditional Heteroskedasticity. An Example. Producer Price Index for Finished Goods

tangia
Download Presentation

Econ 240C

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Econ 240C Lecture 14

  2. ARCH-GARCH Structure?

  3. Outline • Part I: Conditional Heteroskedasticity: example • Part II: Detecting ARCH • Part III: Modeling ARCH & GARCH • Part IV: Estimating GARCH

  4. Part I. Conditional Heteroskedasticity • An Example

  5. Producer Price Index for Finished Goods • April 1947-April 2007 • 1982=100 • Seasonally adjusted rate (SAR)

  6. Transformations • PPI is evolutionary • Take logarithms • Then difference • Obtain the fractional changes, i.e. the inflation rate for producer goods

  7. Stagflation of the 70’s

  8. Modeling dlnppi • Try an arthree

  9. Modeling dlnppi • Try an ARMA(1,1)

  10. ARMA(1,1) Model of Producer Goods Inflation • Residuals from ARMA(1, 1) model are approximately orthogonal but not normal • Are we done?

  11. Part II. Examine Residuals • Trace of residuals • Trace of square of residuals

  12. Resq =resid*resid

  13. Episodic variance • Not homoskedastic • So call heteroskedastic, conditional on dates or episodes when the variance kicks up • Hence name “conditional heteroskedaticity”

  14. Clues • Check trace of residuals squared • Check correlogram of residuals squared • Equation window: View menu, residuals • Check ARCH Lagrange Multiplier Test

  15. ARCH Lagrange Multiplier Test

  16. Clues • Check trace of residuals squared • can get residuals from Actual, fitted, residuals table • Check correlogram of residuals squared • EVIEWS option along with correlogram of residuals • Heteroskedasticity of residuals • Histogram of residuals • kurtotic residuals are a clue

  17. How should we model the conditional heteroskedasticity?

  18. Part III: Modeling Conditional Heteroskedasticity • Robert Engle: UCSD • Autoregressive error variance model

  19. Modeling the error • Model the error e(t) as the product of two independent parts, wn(t) and h(t) • WN(t) ~N(0,1)

  20. Modeling the error • Assume that WN(t) is independent of • So density f{wn(t)*[h(t)]1/2} is the product of two densities, g and k: • f =g[wn(t)]*k{[h(t)]1/2} • And expectations can be written as products of expectations • This is related to writing the Probability of P(A and B) as P(A)*P(B) if events A • And B are independent

  21. Modeling the error • We would like the error, e(t) to have the usual properties of mean zero, orthogonality, and unconditional variance constant • E e(t) = E {[h(t)]1/2*WN(t)} = E{[h(t)]1/2}*E[WN(t)] , the product of expectations because of independence • We may not know E{[h(t)]1/2}, but we know E[WN(t)] =0 so Ee(t)=0

More Related